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Over the past three months, you’d be hard-pressed to find a hotter stock on the market than that of beleaguered tech giant Hewlett-Packard Company (NYSE:HPQ) . That’s not a typo. Since hitting bottom at $11.35 per share on Nov. 20, the stock has shot up 85% to Friday’s close at $21. Investors are beginning to ask: Is the company back?

Remarkably, I’ve seen articles suggesting that this stock can double in a few years, while calling HP a “fallen angel” that can soon take on Apple Inc. (NASDAQ:AAPL) and the rest of the tech world by storm. Really? Now, while the stock’s recovery has indeed been remarkable, let’s not get carried away just yet. Sudden shift in equity sentiment is no indication of success. And nor does it dictate where this company is going. HP still has to execute. And so far, management has not shown that it is capable of realizing any value the business still has left.

How well is Whitman’s “fix and rebuild” progressing?This is what investors have to ask themselves before wondering if the company is back. Investors still forget that HP is in the midst of a five-year “fix and rebuild” plan that CEO Meg Whitman told CNBC about several months ago. For that matter Whitman also advised that investors should not expect to see revenue growth in any segment (except software) until 2014 when new products hit the market.

Although there’s been some progress, and the company has improved its balance sheet, which is now generating as much as $4.1 billion in operating cash flow, I can’t say that this has been enough to spur an 85% run-up in the stock. Rather, a case can be made that HP didn’t deserve such a depressed valuation and the stock was too cheap relative to book value. Essentially, the Street corrected its mistake, which happens all the time.

However, strictly from an operational perspective, first-quarter earnings results suggest that the company is still missing some opportunities. Revenue arrived at $28.4 billion, falling 6% year over year and 5% sequentially. Revenue was down across all segments, which was not a surprise; Whitman had already advised that this would be the case.

The PC business dropped 8% year over year and 6% sequentially. But the rate of the drop was 6% slower than in Q4 (14%). So HP’s new line of ultrabooks could have had some impact. If no news is good news, the rest of the segments did OK. That is to say, they were not any worse off than before. So for a stock that was trading on little-to-no expectations, investors rewarded HP with a “less bad” reaction, which is what’s driving the shares today.

I don’t think there is more near-term upside to these shares. Granted, the “less bad” quarter was rewarded. And HP’s fundamental position assures the company’s viability. But there are still two major problems that management has failed to address. First, the company’s hardware business is not going to stop eroding.

HP doesn’t know how to stop the bleeding. For that matter, there has been no indication that it’s a priority. HP will see more established players like NetApp Inc (NASDAQ:NTAP) , which continues to dominate storage, steal market share. I once pegged NetApp as a great acquisition candidate for Oracle Corporation (NASDAQ:ORCL) , but for the same reasons, HP should make this same consideration.

Big data continues to be an untapped market for HP. And NetApp can close that gap between HP and rivals like Cisco and Oracle. Likewise, HP has missed out on several opportunities to Cisco by failing to synergize its enterprise server and networking businesses. What’s more, Cisco’s software-defined networking initiatives have become major contributors to Cisco’s recent emergence. And unfortunately, this has come at the expense of HP’s declining enterprise footprint.

Finally, management has failed to address mobile. While Whitman cited a five-year process, that’s an eternity in the stock market. No one knows where mobile is going to be next year, much less five. And the situation is grimmer if you haven’t even started. Even Research In Motion Ltd (NASDAQ:BBRY) is struggling to find its way back, and it pioneered the mobile revolution. So what does HP, which has no competitive position, think it can do in that time span to excite investors?

What of the stock?By every measure such as profit margin, revenue growth, earnings growth and a host of other metrics, the stock should be avoided. But the name’s strong and relative to book value, shares seem fairly valued. I don’t see much upside from here until management can realize more value and prove to investors that the company’s brand actually means something again.